UEGO sensor air-fuel ratio determination system and method

ABSTRACT

A method of determining an air-fuel ratio of an internal combustion engine in real-time includes: calibrating sensitivity of a universal exhaust gas oxygen sensor to a plurality of gases; inputting to a universal exhaust gas oxygen sensor controller a molecular composition of Hydrogen, Carbon, Oxygen, and Nitrogen which comprise a combustion fuel in use in the internal combustion engine; calculating with the universal exhaust gas oxygen sensor controller an air-to-fuel ratio by performing a chemical balance equation calculation based on the universal exhaust gas oxygen sensor sensitivity calibration and the input combustion fuel molecular composition; and transmitting the calculated air-to-fuel ratio to an engine control unit inreal-time.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/039,658, filed Mar. 3, 2011, which claims the benefit of U.S.Provisional Application No. 61/310,576 filed Mar. 4, 2010. The entiredisclosure of U.S. Provisional Application No. 61/310,576 isincorporated herein by reference.

BACKGROUND

1. Field

Systems and methods consistent with the present invention relate todetermining air/fuel mass ratio for internal combustion engines, andmore particularly to determining air/fuel mass ratio based on currentsensed from an engine exhaust gas oxygen sensor.

2. Description of the Related Art

The need for increased control of internal combustion (IC) engines hasbeen an ever-present requirement over the evolution of the IC engine.Over the years, control systems targeted to IC engines have become moresophisticated and complex in order to meet the needs of ever-increasingenvironmental and operational constraints. One such area of focusrelates to maintaining an accurate air/fuel mass ratio (AFR) over allengine operational regions. The AFR is initially determined by measuringincoming air to the engine by a mass air flow sensor or by an intakemanifold pressure sensor. The incoming air measurement is then convertedto an air flow using the Ideal Gas Law. A precise amount of fuel isadded to the air based on the known fuel injector flow rate to achievethe desired AFR. The air-fuel charge is then combusted in the engine andexhausted.

However, there are inaccuracies in the actual AFR that may arise frommany sources, and can change during the life of the engine. For example,the airflow sensor can change characteristics due to dirt accumulation,injectors can acquire a varnish coating that changes the actual fuelflow rate, injector spring response can degrade, and fuelcharacteristics and humidity can vary. Hence, there is a need to obtainan independent measurement of the actual AFR, this measurement beingused in a feedback loop that adjusts the injected fuel to more exactlyachieve the AFR which is optimal for the engine conditions at hand.

This independent measurement is made after the mix is combusted using anexhaust gas oxygen sensor. These sensors can be of two types: Narrowband(NB) or Wideband (WB). An NB oxygen sensor simply determines if theexhaust gas is lean (excess oxygen) or rich (all oxygen is bound toanother element). It provides a voltage that is sent directly to anengine control unit (ECU) which then adjusts fuel to maintain astoichiometric ratio. This voltage from the NB sensor indicates that allfree oxygen in the exhaust has been consumed and there is no excess COor H₂.

A WB oxygen sensor, also known as a universal exhaust gas oxygen (UEGO)sensor, provides a measure of the degree of richness and leanness of theair/fuel ratio. This type of WB sensor provides an increased sensorsignal bandwidth to the ECU in order to maintain stoichiometricoperation and optimum catalyst efficiency. In motorsports applications,the UEGO sensor signal provides a direct feedback on the air/fuel ratio(AFR) which can be tailored for a desired mixture.

Another important use of the UEGO sensor signal is to accommodatedifferent fuel mixes. Until recently, the vast majority of passengercars have used only gasoline as a fuel. However, with fossil fuelresources being depleted, many alternative fuels are being pressed intoservice. These fuels include the 10% ethanol/90% gasoline mix nowcommonly sold at most filling stations, and an 85% ethanol mix (E85)that is also becoming popular. These fuels result in a significantlydifferent AFR, both on and off the stoichiometric point. For examplepure ethanol has a stoichiometric AFR of 9.0, while the stoichiometricAFR for regular gasoline is 14.7. It is for this reason that OEMsintroduced special Flex-Fuel sensors in the fuel delivery system toprovide a signal indicating the percentage gas/alcohol mix. Later modelautomobiles use UEGO signals directly in order to determine fuelcomposition mixture in so-called virtual-sensor arrangements.

In motorsport applications the use of alternative fuels is veryprevalent—hydrocarbons such as diesel, ethanol, and nitro-methane arecommon. Oxidizers such as nitrous oxide are also very common.Additionally, water injection is used to reduce the tendency ofdetonation in boost applications. And all of the above can be combinedall at once in various proportions depending on operating situation. Theeffect combining fuels is an altering of the final hydrocarbon andoxygen/nitrogen the engine ultimately has to ignite for combustion. Andsince this fuel combination determines the exhaust gas species molarconcentration, and hence UEGO sensor pump current (to maintain Nernstcell stoichiometry within the sensor head), it is important to take thefuel composition into account. Expensive, lab-grade UEGO sensorcalibration meters allow the entry of hydrocarbon H/C and O/C ratios andhumidity/vapor pressure, but these are fixed quantities and notadjustable in real-time. Lower-cost UEGO sensor controllers do not offerany adjustment in fuel composition, assuming a fixed H/C and O/C fuelfor all conditions.

Existing aftermarket wideband UEGO controllers do not have provisionsfor alternative hydrocarbon fuels or additional sources of oxidizerssuch as N₂0. While the lambda value i.e., the normalized air/fuel rationrelative to the stoichiometric point is a fair approximation for manyfuels, it is not exact because the sensitivities of the UEGO sensor toCO and H₂ have not been taken into account on the rich side of thestoichiometric point, and the error grows as the AFR departs fromstoichiometric on both the lean side and even more on the rich side.

Also, the lambda value is generally less intuitive to users of the WBcontroller for motorsport applications, who are more familiar with theAFR value. While the lambda value can be converted to an AFR, itrequires the user to input the stoichiometric AFR for the fuel beingused. While this can easily be done for pure fuels such as pure gasolineand ethanol, it needs to be calculated for fuel/oxidizer mixes. Forvarying mixes, for example, when a user has a partial tank of gasolineand fills up with E85, calculation of the stoichiometric AFR becomeseven more problematic. Existing aftermarket UEGO sensor controllers donot address this problem, nor do they allow the entry/ implementation ofreal-time hydrocarbon/oxidizer/H₂0 mixtures.

Another limiting aspect with current UEGO sensor controllers availableis the lack of UEGO sensor calibration. The controllers only allow, atbest, calibration in free air, assuming an O₂ content of 20.9% andextrapolating this value for both lean and rich lambda calculation.Other UEGO sensor controllers use a fixed published lambda-vs-pumpcurrent transfer function, valid only for a predetermined gascombination and UEGO sensor. Free-air calibration will yield asatisfactory calibration for lean side of stoichiometric (i.e., excessoxygen, lambda>1), however rich-side operation is not sufficientlycalibrated. In fuel-rich combustion where all oxygen is consumed thereare many gas species remaining, including CO, H₂ and unburned HC. TheUEGO sensor operates by reducing the CO and H₂ into CO₂ and H₂O (i.e.,CO+O₂→2CO₂ and H₂+O₂→2H₂O).

It is apparent that a calibration utilizing oxygen-only will notadequately determine H₂ and CO sensor sensitivities. It should be notedthat in motorsports applications, fuel-rich operation is often desirablesince optimum engine torque output often occurs at regions aroundlambda=0.9. In this case, maintaining stoichiometric operation is not arequirement.

Finally, the actual determination of lambda and AFR from UEGO pumpcurrent readings is not well-defined in aftermarket controllers. Asstated earlier, many controllers utilize default pump current vs. lambdavalues from sensor-head manufacturer data. Of course, the real worldrequires the use of sensor calibration along with knowledge of thehydrocarbon under combustion-both are required for accurate AFR andlambda determination.

Sensor-head calibration is easily accomplished by bench-testing UEGOsensors with known gas compositions, namely O₂, CO and H₂. It should benoted that although the UEGO sensor is also sensitive to unburnedhydrocarbons, the amount of such constituents in the exhaust of a modemengine operating under normal operating conditions is in theparts-per-million range, whereas the concentrations of CO and H₂ areorders of magnitude higher.

The proper way to determine lambda and AFR from a known hydrocarbon fuelis by chemical balance equations. In simple terms, the balance equationkeeps track of the moles (or concentrations or partial pressures) ofeach gas species before and after combustion—nothing is lost and allcomponents have to be accounted for. This calculation can becomplicated, and has been the topic of several technical papers. Mostare targeted for situations where each specific gas component isindividually measured, as is the case with 4 and 5-gas bench analyzers.

For instance a method of calculating lambda value is described in thepaper of J. Brettschneider, “Calculation of the air ratio of air-fuelmixtures and the influence of measurement errors on lambda” in BoschTechnische Berichte, Bd. 6, Heft 4 (1979), pp. 177 to 186. TheBrettschneider calculation has become the standard for lambdacalculation in multi-gas analyzers, although there are comparablecalculations presented in the literature by Silva, Spindt, and Simons.The approaches outlined in each of these papers have the luxury ofseparate and independent measurement of each of the gas constituents. Inother words, there are separate sensor elements which are sensitive togas components O₂, CO, etc. In a UEGO sensor, on the other hand, thereis one sensor element that is responsive to multiple gas components, andhence one measurement. In algebraic terms, there are multiple equations(chemical balance equations) with unknowns, but only one measurement.Hence, relations that yield more information from the one measurementsource are needed. These relations come from the knowledge of thehydrocarbon under combustion and the UEGO sensor element sensitivitiesto specific gas constituents.

Simplifications have been suggested to reduce the computational burdenin order to provide real-time updates, generally in the form of scalingfixed response curves or transfer functions obtained in the most generalcase. This leads to a simplified lambda calculation for fuel-richcombustion and works sufficiently well when the hydrocarbon is fixed, asis the case in a production engine. However, when the fuel types andproportions change, the sensitivities become important and influence thecalculation directly.

SUMMARY

One or more exemplary embodiments provide a method and system fordetermining air/fuel mass ratio.

According to an aspect of an exemplary embodiment, there is provided amethod for determining air/fuel mass ratio based on current sensed froman engine exhaust gas oxygen sensor. The method may include calibratingsensitivity of a universal exhaust gas oxygen sensor to a plurality ofgases; inputting to a universal exhaust gas oxygen sensor controller amolecular composition of Hydrogen, Carbon, Oxygen, and Nitrogen whichcomprise a combustion fuel in use in the internal combustion engine;calculating with the universal exhaust gas oxygen sensor controller anair-to-fuel ratio by performing a chemical balance equation calculationbased on the universal exhaust gas oxygen sensor sensitivity calibrationand the input combustion fuel molecular composition; and transmittingthe calculated air-to-fuel ratio to an engine control unit in real-time.

The method may further include storing in a memory in the universalexhaust gas oxygen sensor controller calibration constants for theplurality of gases resulting from calibrating the sensitivity of theuniversal exhaust gas oxygen sensor.

The method may further include inputting the molecular composition ofthe combustion fuel to the universal exhaust gas oxygen sensorcontroller via a human interface device.

The method may further include inputting the molecular composition ofthe combustion fuel to the controller as an electrical signal from asensor.

The sensor may be one of a humidity sensor, a Flex-Fuel compositionsensor, and a nitrous oxide solenoid open sensor.

The electrical signal may be a digital signal or an analog signal.

The combustion fuel may be mixed fuel.

The molecular composition of the combustion fuel may be input inreal-time by a sensor that senses proportions of mixed fuels.

The method may further include controlling one or more fuel injectors inreal time with the engine control unit based on the transmittedair-to-fuel ratio to adjust fuel delivery to the internal combustionengine to maintain the air-to-fuel ratio.

The air-to-fuel ratio calculation may be performed using a molar balancecalculation.

According to another aspect of an exemplary embodiment, there isprovided a computer-readable recording medium storing acomputer-readable program for executing the method.

According to another aspect of an exemplary embodiment, there isprovided a system or determining an air-fuel ratio of an internalcombustion engine in real-time. The system may include an engine controlunit; a universal exhaust gas oxygen sensor mounted in an exhauststream; and a universal exhaust gas oxygen sensor controller whichreceives a signal from the universal exhaust gas oxygen sensor andperforms a chemical balance equation calculation to calculateair-to-fuel ratio in real-time based on the received signal.

The universal exhaust gas oxygen sensor controller may communicate thecalculated air-to-fuel ratio to the engine control unit in real-time

The engine control unit may provide real-time control of the internalcombustion engine to maintain the air-to-fuel ratio communicated fromthe universal exhaust gas oxygen sensor controller.

The system may further include a human interface device which inputsuniversal exhaust gas oxygen sensor sensitivity calibration data for aplurality of gases to the universal exhaust gas oxygen sensorcontroller.

The system may further include a memory in the universal exhaust gasoxygen sensor controller in which the universal exhaust gas oxygensensor sensitivity calibration data for the plurality of gases arestored.

The system may further include a human interface device which inputs amolecular composition of a combustion fuel in use to the universalexhaust gas oxygen sensor controller.

The molecular composition of the combustion fuel in use may include themolecular composition of Hydrogen, Carbon, Oxygen, and Nitrogen of thecombustion fuel.

The system may further include a sensor which senses and inputs themolecular composition of the combustion fuel to the universal exhaustgas oxygen sensor controller as an electrical signal.

The sensor may be one of a humidity sensor, a Flex-Fuel compositionsensor, and a nitrous oxide solenoid open sensor.

The system may further include a sensor that senses and inputs themolecular composition by proportions of mixed combustion fuels to theuniversal exhaust gas oxygen sensor in real-time.

The engine control unit may control one or more fuel injectors in realtime based on the transmitted air-to-fuel ratio to adjust fuel deliveryto the internal combustion engine to maintain the air-to-fuel ratio.

The air-to-fuel ratio calculation may be performed using a molar balancecalculation.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects and features of the present invention willbe more apparent by describing exemplary embodiments of the presentinvention with reference to the accompanying drawings, in which:

FIG. 1 is a schematic overview of an engine air induction and exhaustsystem according to an exemplary embodiment;

FIG. 2 is a sectional view of an exemplary universal wide band exhaustgas sensor;

FIG. 3 is a flow chart illustrating a method according to an exemplaryembodiment; and

FIG. 4 is a graph illustrating lambda vs pump current for two differentengine fuels according to an exemplary embodiment.

DETAILED DESCRIPTION

Aspects of the present inventive concept provide a system and methodthat use a one-time calibration of the sensitivity of a UEGO sensor tothe gases O₂, CO, and H₂ to directly calculate, in a UEGO sensorcontroller, an air/fuel ratio of an arbitrary air/fuel mix ingested byan IC engine. Factory calibration of the sensitivities of various UEGOsensors to the above three gases is performed, and the resultingcalibration constants are stored in the UEGO sensor controller memory.Together with types and relative volumes/masses of the fuel mixes to beused, the calibration constants are sufficient to provide responseinformation on a particular UEGO sensor. The types and relativevolumes/masses of the fuel mixes may be entered as numerical valuesdirectly into the UEGO sensor controller using a human interface device(HID) or may be provided through an electrical signal from a sensor.This electrical signal may be a simple digital signal denoting theaddition of specific fuel components, or a more information-rich signalsuch as an analog voltage or pulse-coded digital signal.

The fuel composition alteration signal may be used to indicate to theUEGO sensor controller the required fuel mix, so that the calculated AFRwill be correct. No special calibration is needed. Similarly, a humiditysensor may be used to signal the UEGO sensor controller as to thepercentage H₂O in the entering air mixture.

Further, in the racing community, an injection of nitrous oxide may beused to provide boost to a car during the race. Nitrous oxide injectioncan be indicated to the UEGO sensor controller by providing a signalthat the nitrous oxide solenoid is open. This fuel can be factored intothe mix, and again a correct AFR will be provided. A permanent change infuel can also be made, for example from gasoline to propane or LPG.While this would require mechanical modifications to the engine, itwould only require entering the type of the new fuel into the UEGOsensor controller to perform the AFR calculation.

FIG. 1 is a schematic overview of an engine air induction and exhaustsystem according to an exemplary embodiment. Referring to FIG. 1,incoming air 1 to the engine intake manifold 4 is measured by a mass airflow sensor 2 or by an intake manifold pressure sensor 3. The incomingair measurement is then converted to an air flow using a calculationbased on the Ideal Gas Law. An amount of fuel is injected into theincoming air to achieve the desired AFR. The air flow and fuel injectioncalculations are performed by an ECU 14 based on a known flow rate offuel injector 5. The air-fuel charge is then combusted in the enginecylinders 6 and exhausted into the exhaust manifold 7. The molecularcomposition of the exhaust gas 8 is measured by a UEGO sensor 20 inconjunction with a wide band UEGO sensor controller 10.

Molecular composition information of the combustion fuel and calibrationconstants for the UEGO sensor 20 are input to the UEGO sensor controller10 via a human interface device (HID) 16. The HID 16 may be, for examplebut not limited to, an external personal computer, smartphone, orpersonal data assistant which communicates with the UEGO sensorcontroller 10 using a digital or analog data interface. The HID 16allows a user to directly input the calibration constants and/ormolecular fuel composition, including multiple combined fuel sources, tothe UEGO sensor controller 10.

Alternatively or additionally, molecular composition information of thecombustion fuel may be input to the UEGO sensor controller 10 as anelectrical signal from a sensor 18. The sensor 18 may be, for examplebut not limited to, a Flex-Fuel sensor, a humidity sensor, or otherengine sensor.

Calibration constants of the UEGO sensor 20 are stored in the UEGOsensor controller memory 12. Based on the AFR determined from thismeasurement, a correction can be made to the fuel injection by the ECU14 on the next engine fuel injector 5 cycle.

In an NB sensor, oxygen in the exhaust is measured by a “Nernst” cell.The operation of the NB sensor is such that its output is 0.45 voltswhen a balance has been achieved such that there is essentially no freeoxygen in the exhaust, but essentially no unconsumed fuel either. Assoon as the exhaust becomes the least bit rich or lean, the voltage veryrapidly drops toward 0 or jumps toward 1 volt. This change occurs soquickly that a meaningful value for the degree of richness/leannesscannot be obtained. Thus, the NB oxygen sensor effectively provides onlythree discrete outputs: rich, stoichiometric, or lean.

FIG. 2 is a sectional view of an exemplary universal wideband exhaustgas sensor. Referring to FIG. 2, a typical UEGO sensor 20 combines anoxygen-sensing Nernst cell 22 with an “oxygen pump” 21, which isessentially a second Nernst cell, and a reference cell 23 which isexposed to air to create a device that gives a wide range response tovarious air/fuel ratios. The Nernst cell 22 senses exhaust gas oxygen inthe same way as in a conventional NB oxygen sensor. However, thereference cell 23 and the oxygen pump cell 21 are connected in such away that exhaust gas 8 passes through the diffusion gap 24 into the pumpcell 21, and the pump cell 21 either pumps oxygen out of its cavity orpumps oxygen into its cavity so as to achieve a stoichiometric balance.

When the air/fuel mixture is rich, the reference cell 23 produces a highV_(S) voltage 27 (above 0.450 volts). The UEGO sensor controller 10 (seeFIG. 1) reacts to produce a pump current 25 in a “negative” direction toconsume free fuel. When the air/fuel mixture is lean, the reference cell23 produces a low V_(S) voltage 27 (lower than 0.45 volts). The UEGOsensor controller 10 then produces a pump current 25 in the opposite(“positive”) direction to consume free oxygen.

When the air/fuel mixture is at the stoichiometric point, the pump cell21 requires no pump current 25. Since the free oxygen or free fuel hasbeen neutralized, the V_(S) voltage 27 feedback signal goes to about0.45 volts (the stoichiometric reference value).

Measuring the pump current 25 flow and direction required to achievethis balance through a resistor R_(cal) 28 allows the UEGO sensorcontroller 10 to determine the air/fuel ratio at which the engine isoperating. A controlled heater element 26 ensures the UEGO sensor 20 iskept at a nominal operating temperature of 750° C. (˜1400° F.), so thatchanges in the actual exhaust gas temperature do not become a factor inmaintaining a balanced condition in the pump cell 21. The result is aUEGO sensor 20 that can measure lambda ratios (i.e., normalized air/fuelratios relative to the stoichiometric point) from very rich (0.5) toextremely lean (1.5).

The above-described UEGO sensor 20 allows the UEGO sensor controller 10to control the air/fuel mix entering the engine directly. Instead ofswitching the air/fuel mix back and forth from rich to lean to create anaverage balanced mixture, the UEGO sensor controller 10 can simply addor subtract the amount of fuel needed to maintain a stoichiometriclambda of 1.0 or any other ratio.

To provide this fuel, however, the controller 10 must provide the AFR tothe ECU 14, since the AFR, along with the intake air mass (provided by aseparate sensor), are needed to obtain the required fuel mass.

The calculations to be presented describe a method to obtain the AFR forarbitrary fuels and mixes of fuels from the measured pump currentrequired to maintain a UEGO sensor Nernst cell at a fixed 0.45 voltpotential during engine operation. The method only requires acalibration of the system sensitivities to O₂, CO and H₂ gases. Oncethis is calibration is done, the method may be employed in real-time tocalculate the AFR of arbitrary fuels and mixes of fuels without anyfurther calibration.

The exemplary embodiments are based on a balance and re-arrangement ofthe basic combustion equation: Fuel+Air→Combustion Products. Or, asdescribed by equation (1):φ·C_(a)H_(b)O_(c)N_(d)+(xo·O₂+xn·N₂)→v1 CO₂+v2 H₂O+v3 N₂+v4 O₂+v5 CO+v6H₂   (1)

The subscripts a, b, c, and d are inputs describing the fuelcomposition; xo and xn are constants representing the air composition(0.2095 and 0.7905 for oxygen and nitrogen, respectively). The nitrogencan be considered lumped together with argon and other inert componentsin the air. The multiplier φ is the fuel mole fraction relative to amole of air. The fuel mole fraction, along with the fractions vi, whichare also mole fractions relative to a mole of air, can be calculated bybalancing the molecules in equation (1).

For the lean air/fuel mixture case in which there is excess oxygen, itcan be assumed that v5=v6=0, because the excess oxygen preventswater-gas (CO₂) dissociation. The resulting equations (2), (3), (4), and(5) are:Carbon: v1=a φ  (2)Hydrogen: v2=bφ/2   (3)Oxygen: 2v1+v2+2v4=c φ+2xo   (4)Nitrogen: v3=d φ/2+xn   (5)

Combining equation (4) with equations (2) and (3) yields equation (4a):v4=xo−(a+b/4−c/2) φ  (4a)

The usual assumption made at this point is that the fuel/air molarratio, φ, is known, and hence the goal to find the componentcompositions is complete.

A sensor controller according to the exemplary embodiments calculates φfrom the above equations plus the pump current, Ip, from the Nernst cellin a UEGO sensor. The pump current is used to maintain stoichiometricvoltage within the cell by pumping oxygen in or out of the celldepending on the exhaust mixture. The stoichiometry problem is dividedinto a lean side and a rich side, determined by the pump current beinggreater than or equal to zero (i.e., a lean exhaust mixture wherein thecurrent is used to pump free oxygen out of the cell to maintain astoichiometric 0.45 volts) or pump current being less than zero (i.e., arich exhaust mixture wherein current is used to pump oxygen into thecell). Equation (6) is an expression for the lean case:Ip=KO₂.P(O₂)=KO₂.P_(tot) ·v4/Σvi   (6)

In equation (6), KO₂ is a calibration constant obtained from the UEGOsensor by running various concentrations of O₂ through the sensor andmeasuring the pump current, Ip, in milliamps, needed to maintain 0.45 Vin the Nernst cell. The partial pressure of the oxygen, P(O₂), is bydefinition equal to the total pressure, P_(tot), in kPa, times the molefraction of O₂. The latter is v4 divided by the sum of all the molarcomponents:Σvi=x0+xn+(b/4+c/2+d/2)   (6a)

Combining all of the above equations results in equation (7):

$\begin{matrix}{\mspace{50mu}{\Phi = \frac{{xo} - \left( {{Ip}/\left( {{KO}_{2} \cdot P_{tot}} \right)} \right)}{{\left( {{Ip}/\left( {{KO}_{2}{\cdot P_{tot}}} \right)} \right) \cdot \left( {{b/4} + {c/2} + {d/2}} \right)} + \;\left( {a + {b/4} - {c/2}} \right)}}} & (7)\end{matrix}$

From equation (7) the mass air/fuel ratio can be written directly as:

$\begin{matrix}{{{AFR} = \frac{{2\mspace{14mu}{xo}\mspace{14mu}{MO}} + {2\mspace{14mu}{xn}\mspace{14mu}{MN}}}{\Phi \cdot \left( {{a\mspace{14mu}{MC}} + {b\mspace{14mu}{MH}} + {c\mspace{14mu}{MO}} + {d\mspace{14mu}{MN}}} \right)}},} & (8)\end{matrix}$where MC, MH, MO and MN are the molecular weights of carbon C, hydrogenH, oxygen O, and atmospheric nitrogen N₂: 12.011, 1.008, 16, and 14.08,respectively. The final equation for the lean case is equation (8a):AFR=28.964/(φ·(12.011 a+1.008 b+16 c+14.08 d))   (8a)

At the stoichiometric point, Ip=0, since O₂ is neither pumped in or outof the Nernst cell. Hence, from equation (7) with Ip=0 and equation (8):

$\begin{matrix}{{{AFR}\mspace{14mu}{Stoich}} = \frac{28.964 \cdot \left( {a + {b/4} - {c/2}} \right)}{{xo} \cdot \left( {{12.011\mspace{14mu} a} + {1.008\mspace{14mu} b} + {16\mspace{14mu} c} + {14.08\mspace{14mu} d}} \right)}} & \left( {8b} \right)\end{matrix}$

From these equations the air/fuel lambda ratio, λ, can be written as:λ=AFR/AFRStoich=xo/(φ·(a+b/4−c/2))   (8c)

The rich case, indicated by Ip<0, is more complex mathematically becauseof the assumption that v4=0, that is, there is no excess oxygen.However, the basic equation (1) still holds and the balance equationsresult in:Carbon: v1+v5=a φ  (9)Hydrogen: 2(v2+v6) b φ  (10)Oxygen: 2 v1+v2+v5=c φ+2 xo   (11)Nitrogen: v3=d φ/2+xn   (12)

Because there is an extra unknown, another equation is needed. This isthe water balance equation obtained from the dissociation of H₂O and CO₂into H₂ and CO expressed by equation (13):

$\begin{matrix}{{\frac{v\;{2 \cdot v}\; 5}{v\;{1 \cdot v}\; 6} = {Kp}},} & (13)\end{matrix}$where Kp is the equilibrium constant, a function of exhaust temperature.For a typical value of 1740 K, Kp is 3.5.

The measured sensor current for the rich case is given by equation 14:Ip=−KCO.P(CO)−KH₂.P(H₂)=−(P _(tot) /Σvi)·(KCO v5+KH₂ v6),   (14)which includes two additional sensitivity calibrations, KCO and KH₂.Substituting in the component expressions from equations (9) to (12),yields equation (15):Σvi=xn+(a+b/2+d/2) φ  (15)

Also, from equations (9) to (11), v1, v2, and v6 can be written in termsof v5 and φ as follows:

From equation (9), v1=aφ−v5.

From equation (11), v2=cφ+2 xo−2 v1−v5=cφ+2 xo−2 aφ+v5.

From equation (10), v6=(bφ/2)−v2=(bφ/2)−cφ−2 xo+2 aφ−v5.

Inserting v6 and equation (15) into equation (14) and solving for theunknown component, v5, equation (16) can be written as:v5=−[((xn Ip/P _(tot))−2 xoKH₂)/(KCO−KH₂)]−[((Ip/P_(tot))·(a+b/2+d/2)+KH₂(2a+b/2−c))/(KCO−KH₂)]·φ=C51+C52·φ  (16)where C51 and C52 are convenience terms of known or measured quantities:C51=−[((xn Ip/P_(tot))−2 xo KH₂)/(KCL−KH₂)]  (16b)

The four terms on the left side of the water balance equation (13) arenow in terms of φ. Cross multiplying, quadratic equation (17) isobtained:Aφ ² +B φ+C=0,   (17)where A, B, and C are defined as:A=[−Kp(a−C52)·(C52−(2a+b/2−c))+C52·((2a−c)−C52)]  (17(a)B={Kp [C51·(C52−(2a+b/2−c))−(2 xo+C52)·(a−C52)]+C51·((2a−c)−C52)−C52·(2xo+C52)}  (17b)C=C51·(2 xo+C51)·(Kp−1)   (17c)

The sign of the radical in the solution of equation (17) is taken tomake φ come out positive. The case KCO=KH₂ typically does not occur inpractice because the sensitivities to CO and H₂ are quite different. Inany case, the KCO=KH₂ equality simplifies equation (16) and φ can besolved for directly. The AFR and lambda ratio, λ, are then obtained fromequations (8a) to (8c) which apply to the rich case as well.

Exemplary embodiments provide the capability of working with severaldifferent concurrent fuel sources in combination. For example, given amix of fuels by percent weight, each fuel may be represented as W_(i)with composition C_(ai) H_(bi) O_(ci) N_(db), where the W_(i) add up to100%. Such a mixture can be represented as a single fuel of the form:C_(a) H_(b) O_(c) N_(d), as follows.

The molecular weights of the fuels can be written as:Mi=ai MC+bi MH+ci MO+di MN,   (18)MC, MH, MO and MN again being the molecular weights of carbon C,hydrogen H, oxygen O, and atmospheric nitrogen N2: 12.011, 1.008, 16,and 14.08, respectively. The mixed fuel molecular composition is then:a=Σ[(W _(i) ·ai)/M _(i)],   (19a)b=Σ[(W _(i) ·bi)/M _(i)],   (19b)c=Σ[(W _(i) ·ci)/M _(i)],   (19c)d=Σ[(W _(i) ·di)/M _(i)],   (19d)the sums being over all the fuel types in the mix. W_(i) can remain as apercentage because it is an appropriate scaling, and the relativenumbers of the elements are of more importance. The carbon ratios forthe fuel elements can be obtained by dividing b, c, and d by a, andsetting a equal to 1. Thus, C_(a) H_(b) O_(c) N_(d) is equivalent to CH_(b/a) O_(d/a) N_(d/a) and the subscripts are termed the H/C, O/C andN/C ratios.

If the mixture is specified by fuel volumes V_(i) with densities ρ_(i),then the weight fractions can be calculated as shown by equation 20:W _(i)/100=mass_(i)/Σ(mass_(i))=Σ_(i) ·V _(i)/Σ(Σ_(i) ·V _(i))   (20)and the preceding equations used.

Various “fuels” can be specified, such as water (H₂O) in the form ofhumidity or deliberate water injection, and Nitrous Oxide (N₂O), bysetting ai=0 and bi or di=0 as appropriate. It can easily be seen thatthe method can accommodate practically any mass combination of fuel andoxidizer. As long as the composition mass of each component is known andpresented to the UEGO sensor controller at the time of combustion, anaccurate ratio of air to fuel can be determined in real-time.

Also, experimental engine setups are known which utilize oxygen (O₂) gassources that are introduced to the engine in addition to the incomingintake air to act as an enhanced oxidizer. With the exemplaryembodiments, it is possible to account for the addition of extra oxygen.Referring back to equation (1), the incoming air ratio of oxygen (xo)and nitrogen (xn) can be altered to account for the extra oxygen—the sumof xo and xn is equal to one so additional O₂ will have the effect ofreducing the content of N₂.

FIG. 3 is a flow chart illustrating a method according to an exemplaryembodiment. The method uses the sensed pump current from a UEGO sensorto calculate AFR for arbitrary fuels and mixes of fuels which may beused for internal combustion engines. The sensing and control of thepump current and the calculation of AFR are done in a UEGO sensorcontroller, which may be separate from, or a part of an ECU.

Referring to FIG. 3, the fuel composition is first determined (S300).The fuel composition may be determined either from fixed inputs, whichcould be constant and hence only a one time calculation would be needed,or from sensor read backs from, for example but not limited to,flex-fuel sensors, or water injectors, or nitrous oxide injectors, thatprovide the percentage composition of the fuel mixture. The UEGO sensorcontroller 10 waits for the ECU 14 to transmit a signal instructing theUEGO sensor controller 10 to begin calculation of the AFR (S310-N). Thesignal may be sent because fuel injection is needed or it may be sent ata periodic rate independent of engine cylinder events. Upon receivingthe calculate signal from the ECU 14 (S310-Y), the UEGO sensorcontroller 10 obtains UEGO sensor pump current 25 (S320). In thebackground, the UEGO sensor pump current 25 is continuously adjusted bythe UEGO sensor controller 10, and the UEGO sensor pump current 25 valueis read by the UEGO sensor controller 10 at this time. The equationsdescribed above are then solved for the AFR and lambda values (S330).The AFR and lambda values thus obtained are then transmitted to the ECU14 for correction of the fuel mass on the next scheduled injection.

In another exemplary embodiment, the method may be embodied on acomputer readable medium as a program for causing, when executed,hardware, for example but not limited to, a computer, a processor, aField-Programmable Gate Array (FPGA), or an Application-SpecificIntegrated Circuit (ASIC) to execute the operations of the method. Thecomputer readable medium may be, for example but not limited to,magnetic storage media, optical storage media, and solid state storagemedia, for example but not limited to, flash memory, volatile memory,non-volatile memory, and programmable memory.

FIG. 4 is a graph illustrating lambda vs control pump current for twodifferent engine fuels according to an exemplary embodiment. Referringto FIG. 4, curves of results of calculated lambda values from the methoddescribed herein when applied to two fuels, regular gasoline andnitromethane, are shown. As can be seen in FIG. 4, the difference inlambda values between the two fuels is significant, about 2% on the leanside and 3% at the extreme rich side. This difference is not accountedfor by current aftermarket controllers, and the error translatesdirectly into an error in the AFR and hence the fueling of the engine.

The method herein has been described in the context of a separate UEGOsensor controller configuration. In actual implementation there is norequirement for the UEGO sensor controller to be a separate controller.A combination of the ECU and the UEGO sensor controller into one unit ispractical and does not limit the novel aspects of the inventive concept.Additionally, the means by which the instantaneous fuel composition isprovided to the exemplary embodiments (e.g., user-input, digital,analog) does not limit the scope or application of the inventiveconcept.

Existing aftermarket WB Controllers which are meant for in-car use withan ECU have provision only for free air calibration, and compute an AFRvalue which applies only to gasoline. The systems and methods of theexemplary embodiments allow calibration, at the factory or by the enduser, of the sensitivity of the UEGO sensor to O₂, CO, and H₂ gases. Themolecular composition(s) of the fuel(s) being used can be input, and,with no further calibration the correct AFR will be calculated for aspecific fuel or fuel mix. Calculation utilizes chemical balancerelations based on hydrocarbon and measured sensor sensitivities. Themolecular composition can also be provided in real time by, for example,a Flex-Fuel composition sensor which senses the proportion of mixedfuels.

Although a few embodiments of the present inventive concept have beenshown and described, it should be appreciated by those skilled in theart that changes may be made to exemplary embodiments without departingfrom the principles and spirit of the invention. Also, the descriptionof the exemplary embodiments of the inventive concept is intended to beillustrative, and not to limit the scope of the claims, and manyalternatives, modifications, and variations will be apparent to thoseskilled in the art.

What is claimed is:
 1. A method of determining an air-fuel ratio of aninternal combustion engine in real-time, the method comprising:calibrating sensitivity of an oxygen sensor to a plurality of gases;inputting to a processor a molecular composition of a combustion fuel inuse in the internal combustion engine; calculating an air-fuel ratio inreal-time by performing a chemical balance equation calculation; andcontrolling one or more fuel injectors of the internal combustion engineby transmitting the calculated air-fuel ratio to an engine control unitthat implements the calculated air-fuel ratio in real-time.
 2. Themethod of claim 1, wherein the calculating the air-fuel ratio inreal-time by performing the chemical balance equation calculationcomprises performing the chemical balance equation calculation based onthe oxygen sensor sensitivity calibration and the input combustion fuelmolecular composition.
 3. The method of claim 1, wherein the inputtingthe molecular composition of the combustion fuel comprises inputtingrespective portions of hydrogen, carbon, oxygen, and nitrogen.
 4. Themethod of claim 1, wherein the inputting the molecular composition ofthe combustion fuel comprises inputting a known percentage of each of aplurality of different hydrocarbon fuels.
 5. The method of claim 4,wherein the inputting the molecular composition of the combustion fuelfurther comprises inputting a known mass percentage of N₂O.
 6. Themethod of claim 4, wherein the inputting the molecular composition ofthe combustion fuel further comprises inputting a known mass percentageof O₂.
 7. The method of claim 1, wherein the inputting the molecularcomposition of the molecular composition of the combustion fuelcomprises inputting fixed values of the combustion fuel components. 8.The method of claim 1, wherein the inputting the molecular compositionof the molecular composition of the combustion fuel comprises obtainingvalues of signals received from sensors that monitor percentagecomposition of the combustion fuel in real-time.
 9. The method of claim8, wherein the received signals comprise at least one of a flex-fuelsensor signal, a water injector sensor signal, and a nitrous oxideinjector sensor signal.
 10. The method of claim 1, wherein the processoris an oxygen sensor controller.
 11. The method of claim 1, wherein theoxygen sensor is a universal exhaust gas oxygen (UEGO) sensor.
 12. Atangible computer readable medium having embodied therein a program forcausing a processor to execute a method of determining an air-fuel ratioof an internal combustion engine in real-time, the program includingoperations comprising: calibrating sensitivity of an oxygen sensor to aplurality of gases; inputting to the processor a molecular compositionof a combustion fuel in use in the internal combustion engine;calculating an air-fuel ratio in real-time by performing a chemicalbalance equation calculation; and controlling one or more fuel injectorsof the internal combustion engine by transmitting the calculatedair-fuel ratio to an engine control unit that implements the calculatedair-fuel ratio in real-time.
 13. The tangible computer readable mediumhaving embodied therein a program as defined in claim 12, wherein thecalculating the air-fuel ratio in real-time by performing the chemicalbalance equation calculation comprises performing the chemical balanceequation calculation based on the universal exhaust gas oxygen sensorsensitivity calibration and the input combustion fuel molecularcomposition.
 14. The tangible computer readable medium having embodiedtherein a program as defined in claim 12, wherein the inputting themolecular composition of the combustion fuel comprises inputtingrespective portions of hydrogen, carbon, oxygen, and nitrogen.
 15. Thetangible computer readable medium having embodied therein a program asdefined in claim 12, wherein the inputting the molecular composition ofthe combustion fuel comprises inputting a known percentage of each of aplurality of different hydrocarbon fuels.
 16. The tangible computerreadable medium having embodied therein a program as defined in claim15, wherein the inputting the molecular composition of the combustionfuel further comprises inputting a known mass percentage of N₂O.
 17. Thetangible computer readable medium having embodied therein a program asdefined in claim 15, wherein the inputting the molecular composition ofthe combustion fuel further comprises inputting a known mass percentageof O₂.
 18. The tangible computer readable medium having embodied thereina program as defined in claim 12, wherein the inputting the molecularcomposition of the molecular composition of the combustion fuelcomprises inputting fixed values of the combustion fuel components. 19.The tangible computer readable medium having embodied therein a programas defined in claim 12, wherein the inputting the molecular compositionof the molecular composition of the combustion fuel comprises obtainingvalues of signals received from sensors that monitor percentagecomposition of the combustion fuel in real-time.
 20. The tangiblecomputer readable medium having embodied therein a program as defined inclaim 19, wherein the received signals comprise at least one of aflex-fuel sensor signal, a water injector sensor signal, and a nitrousoxide injector sensor signal.